(a) Field of the Invention
The present invention relates generally to coding schemes for communication systems and, more particularly, to half rate block coded modulation schemes for use in Rayleigh fading channels.
(b) Description of Related Art
Hamming distance and product distance are two well known metrics used to measure the "separation" of communication symbols. In general, the amount of separation corresponds to the ease with which communication symbols will be confused. The Hamming distance represents the number of symbols that are different between two code words. For example, the Hamming distance between binary code words 010 and 101 is three, and the Hamming distances between 010 and 000 is one. The greater the Hamming distance between two code words the less likely that the code words will be confused.
Euclidean distance is the measurement of the separation between transmitted code words in a communication system. Specifically, it is the measure of the distance between two symbols on the communication code word bit map. In a 8 phase shift keying communication system, for example, if a carrier phase of 0 represents the code word 001 and a carrier phase of 180 represents code word 011, the code words have maximum Euclidean distance. Conversely, if the code word 001 is represented by a word 011, the code words have maximum Euclidean distance. Conversely, if the code word 001 is represented by a phase of 0.degree., and the code word is 100 is represented by a phase of 45.degree., the Euclidean distance is a minimum.
Two typical communication channel models are Gaussian and Rayleigh channels. A Gaussian channel is modeled as a channel having an additive noise factor. In a Gaussian channel the power received is essentially the power transmitted reduced by a distance attenuation factor and a noise power component. When attempting to send information through a Gaussian channel it is useful to maximize the Euclidean distance between code words to alleviate confusion between the transmitted phases. However, it is not particularly helpful to maximize Hamming distance because signal power is usually adequate to determine the information contained in the phase of the transmitted signal.
A Rayleigh communication channel is characterized as a fast fading channel having multipath communication components that interact constructively and destructively. The multipath components can cause the power received to decrease to zero. Since receive power can drop out completely in a Rayleigh channel, Euclidean distance in not critical because the underlying principle behind Euclidean distance is the elimination of the confusion between the phases of the various received signals. In a Rayleigh channel the signal may not even be present. Therefore, the Hamming distance is critical to system operation. If the Hamming distance between two signals is large, even partial loss of the received signal may not inhibit the determination of the transmitted code word.
The Rayleigh channel model is commonly used when designing a mobile communications system such as cellular or wireless local network systems. A known coding scheme developed to function in a Rayleigh channel is the trellis coding modulation scheme. Trellis coding has three main features. First, trellis coding provides additional points in the communications constellation for redundancy and forward error correction. Second, trellis coding uses convolutional coding to introduce dependency between successive signal points, such that only certain signal patterns are permitted in the system. Third, soft decision coding is performed at the receiver in which the permissible sequence of signals is modeled as a trellis structure. Trellis coding has the disadvantage of being computationally intensive and, therefore, slow and occasionally difficult to implement in systems not having large computational capacity.
Thus, it would be desirable to have a coding scheme for use in a Rayleigh channel that is fast, computationally simple, and can be easily implemented.